What's your choice? Learning the mixed multi-nomial logit model

Ammar Ammar, Sewoong Oh, Devavrat Shah, Luis Filipe Voloch

Research output: Contribution to journalConference articlepeer-review


Computing a ranking over choices using consumer data gathered from a heterogenous population has become an indispensable module for any modern consumer information system, e.g. Yelp, Netflix, Amazon and app-stores like Google play. In such applications, a ranking or recommendation algorithm needs to extract meaningful information from noisy data accurately and in a scalable manner. A principled approach to resolve this challenge requires a model that connects observations to recommendation decisions and a tractable inference algorithm utilizing this model. To that end, we abstract the preference data generated by consumers as noisy, partial realizations of their innate preferences, i.e. orderings or permutations over choices. Inspired by the seminal works of Samuelson (cf. axiom of revealed preferences) and that of McFadden (cf. discrete choice models for transportation), we model the population's innate preferences as a mixture of the so called Multi-nomial Logit (MMNL) model. Under this model, the recommendation problem boils down to (a) learning the MMNL model from population data, (b) finding am MNL component within the mixture that closely represents the revealed preferences of the consumer at hand, and (c) recommending other choices to her/him that are ranked high according to thus found component. In this work, we address the problem of learning MMNL model from partial preferences. We identify fundamental limitations of any algorithm to learn such a model as well as provide conditions under which, a simple, data-driven (non-parametric) algorithm learns the model effectively. The proposed algorithm has a pleasant similarity to the standard collaborative filtering for scalar (or star) ratings, but in the domain of permutations. This work advances the state-of-art in the domain of learning distribution over permutations (cf. [2]) as well as in the context of learning mixture distributions (cf. [4]).

Original languageEnglish (US)
Pages (from-to)565-566
Number of pages2
JournalPerformance Evaluation Review
Issue number1
StatePublished - Jun 20 2014
Externally publishedYes
EventACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2014 - Austin, United States
Duration: Jun 16 2014Jun 20 2014

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications


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